Alpha-relaxation of an isotropic petroleum pitch: A controlled stress and strain oscillatory rheometry study

Carbon Vol. 35, Pergamon

No. 7, pp. 1013-1021, 1997 0 1997 ElsevierScienceLtd

Printed in Great Britain. All rights reserved 0008-6223197 $17.00+ 0.00 PII: SOOOS-6223(97) 00063-8

ALPHA-RELAXATION OF AN ISOTROPIC PETROLEUM PITCH: A CONTROLLED STRESS AND STRAIN OSCILLATORY RHEOMETRY STUDY X. PY,* E. DAGUERRE, A. GUILLOT and B. SPINNER C.N.R.S.-I.M.P.,

Institut de Science et Gtnie des Matdriaux et Pro&d&, 66860 Perpignan

52 avenue de Villeneuve,

cedex, France

(Received 12 December 1996; accepted in revised form 25 March 1997) Abstract-Oscillatory measurements under controlled stress and controlled strain have been performed on the Ashland A240 isotropic petroleum pitch using a cone/plate rheometer. The storage and loss components of the modulus of rigidity have been analysed by means of time-temperature superposition coupled with the Williams, Landel and Ferry ( WLF) procedure. Loss modulus results obtained under controlled stress are in good agreement with those previously published on the same material but using a plate/plate geometry (Turpin et al., Carbon, 1994, 32, 225). The temperature-dependence of the storage modulus presents a three decades a-relaxation step at T. = 114°C followed by a corresponding 11 units peak of tan (6) at r,= 124°C. Such cc-relaxation has been extensively studied for amorphous polymers

and other glassy materials within the glass transition temperature range but, up to now, has not yet been studied for pitches. Characteristic relaxation time t, similar to t,,, has been calculated within the investigated experimental temperature range and correlated by the Tammann-Vogel-Fulcher (TVF) equation. The corresponding TVF parameters are within the same order of magnitude of those encountered in amorphous polymers. A detailed analysis of the applicability of the WLF method is presented. Same values for the storage and loss modulus shift factors are obtained at low temperature up to T,. At higher temperature, storage modulus shift factor presents a change of regime and a strong deviation from loss shift factor. Therefore, with respect to the a-relaxation phenomenon, the applicability of the WLF procedure to an isotropic pitch is only possible at a temperature below T,. 0 1997 Elsevier Science Ltd Key Words-A.

Isotropic

petroleum

pitch, C. oscillatory

rheometry,

D. r-relaxation.

time-temperature superposition coupled with the Williams Landel Ferry ( WLF) analysis extensively used for polymers. In the method of reduced variables procedure, the criteria for applicability are [ 111: 1) exact matching of the shapes of adjacent curves, 2) the same shift factor aT values must superpose all the viscoelastic functions, 3) the temperature dependence of ar must have a reasonable form consistent with experiments. In the present work, a detailed analysis on the applicability of the WLF method is presented with respect to the three above mentioned criteria. The authors have studied the viscoelastic behaviour of the Ashland A240 isotropic pitch under both controlled stress and controlled strain conditions using a cone/plate geometry. A comparison of the obtained results with those published elsewhere by other authors [ 1,9] on the same material but with other geometries is presented. Moreover, the first analysis of the tlrelaxation of isotropic petroleum pitch is done and the characteristic parameters of this phenomena compared to those published for amorphous polymers.

1. INTRODUCTION

For 20 years, extensive work has been focused on the rheological characteristics of pitch material. Numerous papers have described viscosity-temperature behaviour from apparent steady-flow viscosity measurements. Various conclusions were published depending on the experimental procedure and the system used. As reported by Rand [2] in his extensive review on rheological aspects of pitches, these materials are pseudo-Newtonian systems showing evidence of viscoelasticity through Weissenberg effect and die swell measurements [3]. Nevertheless, only a few recent papers were concerned with transient experiments: torsional creep [4], controlled stress oscillatory [ 1, $61 and controlled strain oscillatory [7-lo] tests. Those few studies are not easy to compare: the controlled stress and strain experiments were obtained using different geometries (plate/plate and cone/plate) and different materials (isotropic or mesophased petroleum or coal tar pitches). Moreover, as such useful techniques provide viscoelastic data needed for industry, more efforts and especially generalised information have to be obtained in this area. Turpin et al. [l], have shown that viscoelastic properties (loss modulus, storage modulus and dynamic viscosity) are well superposed using the

2. APPARATUS

AND MEASUREMENT

The experimental investigation using a Physica-Rheolab MC100

*Corresponding author. 1013

was performed rheometer under

1014

x. PY erul

both controlled stress or controlled strain test procedures. Measurements presented in this paper were made at temperatures in the range of 95 to 160°C and at frequencies in the range of 1 to 101 rad ‘s-i using a standard cone/plate geometry: a stationary measuring plate (2.5 x 10m2 m in diameter) and the measuring cone (1’ in cone angle) of stainless steel. Controlled stress tests were done for 18 different temperatures while strain controlled tests were done for 10 different temperatures. In order to prevent any temperature-dependent extension effect of the stainless steel parts of the cone/plate geometry, the gap width was adjusted at each working temperature to the fixed value of 50 x lO-6 m prior to any frequency-scan isothermic experiment. Nevertheless, some temperature-scan isochronal tests were also performed over a limited range of temperatures. Depending on the working temperature, an adjusted amount of sample (from 150 x 10d6 to 170 x lOA kg) was used in order to fill correctly the cone/plate gap. Therefore, no effect of the sample load was detected on the viscoelastic measurements. The raw pitch sample was placed on the centre of the heated plate and permitted to melt, no treatment was imposed to the material before measurement. When the desired steady-state temperature was reached, the upper part of the geometry was slipped downwards and the pitch sample subjected to a slight steady flow in order to reach an homogeneous filling of the gap and left to rest. Then, frequency-scans were conducted over the range 1 to 101 rad . sm’ under a selected stress or a selected strain within the linear viscoelastic region [I]. To prevent possible oxidation of the pitch, nitrogen flow was maintained throughout the experiment in the rheometer chamber. Further, high temperature experiments (from 140 to 160°C) were repeated in the presence of air. As those last results were similar to those obtained under nitrogen, no reticulation effect was detected in the experimental temperature range.

3. SAMPLE STUDIED In order to compare directly the obtained experimental results with those previously published by other authors [1,9] on other geometries, it seemed appropriate to test the same Ashland A240 isotropic petroleum pitch they had used. Various basic data of this widely-studied material (analysis and manufacturer’s viscosity data) are gathered in Table 1 of the referenced paper [ 1 ]

viscoelastic region, the strain (resp. stress) will also alternate sinusoidally but will be out of phase with the stress (resp. strain). Writing the equations in their complex forms z= ro e’wt ./+,o

(1)

e”WL+d’

(2)

where d is the phase-lag. The viscoelastic linear differential equation is transformed into the following complex linear algebraic equation

T(t) = G(w);‘(t)

(3)

Where G(O) is the complex modulus reciprocally related to the complex compliance J(O). A knowledge of one of these functions is sufficient to characterise the viscoelastic behaviour of the material. Following the usual choice and for easy comparison with literature, we will use the complex modulus G(w) = G’(w) + iG”(w)

(4)

The complex modulus is composed of its real part, the storage (or elastic) modulus G’ and its imaginary part, the loss (or viscous) modulus G”. G’ is representative of the elastic energy stored by the material per cycle reversively and G” is a measure of the energy dissipated or lost as heat by viscous flow per cycle of sinusoidal deformation. The phase-lag 6 can be calculated as follows G”(ta) tan(&) = ~ G’(w)

(5)

The loss tangent tan (6) is a measure of the ratio of energy lost to energy stored in a cyclic deformation. It can often be more conveniently measured than any other viscoelastic function and is of considerable practical interest [ 111. However, it is less susceptible to direct theoretical interpretation than the other functions. Typically G’(w) = 0, G”(w) = G and 6 = 7r/2 for a Newtonian viscous liquid while G’(o)= G, G”(w) = 0 and 6 = 0 for an elastic solid. All systems presenting an intermediate behaviour with both moduli varying with the frequency and the phase-lag between 0 and 7r/2 are classified as viscoelastic materials. The complex viscosity can be calculated as follows

l(1)

the real part thus

of which

is the dynamic

viscosity

q’,

I, 4. DYNAMIC MEASUREMENTS In dynamic measurements, the stress r (resp. strain 7) is varied periodically, usually with a sinusoidal alternation at a frequency w. A periodic experiment at the frequency o is qualitatively equivalent to a transient experiment at time t= wvl. In the linear

+G cu

(7)

As dynamic measurements at very low frequency tend to shear measurements, this dynamic viscosity is seen as analogous to the shear viscosity at a limiting frequency of 0.

Alpha-relaxation 5. RESULTS 5.1

of an isotropic

AND DISCUSSION

Viscoelastic parameters isotherms

Controlled stress oscillatory rheometry experiments lead to typical viscoelastic parameters G’ and G” curves presented in Figs 1 and 2 respectively for 8 selected temperatures. Loss modulus curves obtained under controlled stress are similar to those already presented for the same material in the literature [l]. Such curves corresponding to G’ are not available in the literature. Therefore, no comparison of raw data is possible for this modulus. Moreover, the data obtained under controlled stress and controlled strain (not presented here for legibility) superposed fairly well on each other. This confirms that, taking into account some experimental error, those two experimental procedures can be considered as

petroleum

pitch

1015

equivalent. Nevertheless, high temperature (and therefore low frequency) controlled strain results are more scattered than those obtained under controlled stress. Therefore, controlled stress procedure was mainly preferred and the corresponding results were used for calculations in the present paper. Except at the two lower temperatures, the G’ and G” moduli decrease with increasing temperature and lower frequency and the corresponding curves are roughly parallel to each other. At the two lower temperatures, G” presents a maximum value while G’ tends to an asymptotic one. An original result appears in the particular behaviour of the G’ modulus at temperatures above 120°C: the G’ isotherms tend to stack together while G” isotherms still present significant difference.

5.2 cc-relaxation (or primary relaxation) phenomenon 5.2.1 Relaxation phenomenon. In a system

%

I___.

-- --..

I -0.5

0.0

0.5

/. 110°C

r

0 120°C

1

0140.7 . 149.8"C' 133°C "C I d 160°C

1.0

1.5

2.0

2.5

logkd

Fig. 1. Storage modulus as a function of both the temperature and the oscillation frequency (selected experiments done under controlled stress).

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

log(o)

Fig. 2. Loss modulus as a function of both the temperature and the oscillation frequency (selected experiments done under controlled stress).

where a certain coherence exists between molecules, a deformation will cause a certain mutual displacement of them. For slight displacements, one may imagine that the molecules will not change their relative positions. The intermolecular field of force will be disturbed and the system will absorb a quantity of potential energy which will give rise to internal tensions in order to balance the external forces. During the release of these external forces, the internal tensions tend to bring the molecules back to their original positions. The original structure of the material is restored by consumption of absorbed potential energy. In this case, the material is truly elastic. As soon as an impulse due to the thermal agitation has the same energy content as the energy with which the intermolecular field of force has been disturbed, it is evident that the molecule may be forced back into its position with smaller energy content. The stored potential energy will then be transformed into heat. In this way, the internal tensions in the material disappear, and a continual decrease of the tension will be necessary to keep the material in its deformed state. This phenomenon is called relaxation. Under any stimulus (mechanical stress, etc.) a glassy material answers through configurational changes and two different relaxation phenomena can be observed, _ the a-relaxation for which the molecular mobility becomes generalized as a result of the glass-transition, _ the j-relaxation resulting of local movements. Those phenomena are observed at T, and TO characteristic temperatures mainly dependent of the working frequency. Nowadays, it is well established that the cc-relaxation shows universal features regardless of the type of glassy-forming system considered: ionic, low molecular weight organic, inorganic, polymeric, etc. These characteristic features are [ 12,131: (d) the non-Debye behaviour observed in fre-

X. Pu et al

1016

quency or time dependence of the characteristic parameters, (e) the non-Arrhenius temperature-dependence of the characteristic relaxation time. As isotropic petroleum pitches belong to low molecular weight organic materials, those two features have to be observed for a possible identification of an a-relaxation phenomenon. 5.2.2 Experimental evidence_ The cc-relaxation is usually observed for amorphous polymers close to the glass transition [12,14,15]. It can be illustrated by isochronal plots of G’, G” and tan (6). In Figs 3-5 such isochrones obtained at 101 rad. s-l are presented for A240 pitch under controlled stress (Fig. 3) and controlled strain (Fig. 4). Usually, for amorphous polymers, tan (6) peak amplitude is within the 6 to 30 units range and

12

10

0

strain

.

stress

-Tdecrease ...---Tincrease

8 e

F b

F B

6 4

2

0 80

100

120

140

160

180

TV9 7

Fig. 5. Controlled stress and strain tan (6) isochrones temperature-scans at 101 rad. s-l.

-

G'decrease

.---.. G'increase '

6

~ -. 0

G" decrease1 I G"increase w-scanG'

% 100

80

120

140

l

160

160

T (“C) Fig. 3. Controlled stress loss and storage moduli and temperature-scans at 101 rad.s-‘.

isochrones

_1

80

100

120

140

160

180

TN)

Fig. 4. Controlled

and

strain loss and storage at 101 rad.s-‘.

moduli isochrones

the G’ step within a three decades amplitude [ 151. Illustrating once more the similarity with amorphous polymers, the obtained amplitudes of A240 isotropic pitch are strictly in the same order of magnitude: the storage modulus a-relaxation step presents a three decades amplitude within a 20°C temperature range and the tan (6) an 11 units amplitude peak. The inflexion point temperature of the G’ step has been estimated as T, = 113°C and T, = 115°C for controlled stress and controlled strain measurements, respectively; T, = 114°C will be taken as a mean value. The cr-relaxation phenomenon proceeds through a temperature range as glass transition does, it is not a first-order transformation. The corresponding peak of the loss tangent is observed at T,= 124°C which corresponds to the end of the storage modulus step. For temperatures above 13O”C, the flow of material is observed in Figs 3 and 4 as it is for amorphous polymers [ 141. Moreover, those two figures illustrate good agreement between controlled stress and controlled strain measurements. 5.2.3 a-relaxation, softening point and glass transition. It has been argued that the Ring and Ball softening point is approximately an isoviscous temperature at which the viscosity equals lo3 Pa. s. As a matter of fact, the temperature at which the isotropic A240 viscosity reaches such a value is 120°C a value very close to its softening point rs = 119°C [ 11. T, does not have as precise a significance as the melting point and glass transition point. Moreover, as it is for T,, it has been pointed out that different methods of measurement give different values of softening point. Softening point has been used as one of the most useful and convenient measures for flow behaviour of pitches [4]. Those experimental and conceptual approaches associated with T, are basically different to those temperatures

Alpha-relaxation

of an isotropic

of T, and Tg.Therefore, and as mentioned by Perez [ 151 in the extensive review about amorphous polymers, those parameters do not have to be confused even if, as in our case, their respective values can be very close to each other. The fundamental significance of the glass transition region is the region in which relaxation processes change rapidly with respect to the experimental time scale. It has to be considered as the temperature range at which the molecular mobility characteristic characteristic time time rmol and the experimental texpare of the same order of magnitude. Therefore, the pertinent parameter for the so-called glass-transition should be r,,, which represents the time needed for any structural unit to move from a distance equivalent to its own dimension. Then, Tg has to be considered as a temperature range where, during cooling, the supercooled melt falls out of the equilibrium-like state and, therefore, a glassy material is obtained. In this temperature range, a non-linear behaviour of the different parameters characterizing the system is widely observed [ 121. The glass transition temperature Tg of A240 isotropic pitch has been measured using different experimental procedures: differential scanning calorimetry (DSC), broad line proton MNR and penetrometry. Those measurements lead to different values for the same material depending on the technique and the analysis of the obtained curves. The experimental characteristic time effect has been clearly observed by workers measuring Tg using differential scanning calorimetry. As reviewed by Barr et al. [ 161 the thermical scans exhibit an endotherm in the vicinity expected for Tg attributed to a partial structural ordering similar to crystallization in polymers [ 171. In a second scan made immediately after cooling the sample rapidly, the peak was absent but a baseline shift was observed at a temperature lower than the initial peak [ 14,151. This shift is characteristic of the glass transition in material. A A240 sample was amorphous re-investigated after storage for a period of 1 month following the second DSC quenching [ 151. The peak reappeared but was reduced in area. This experimental observation illustrates the importance of time scale and relaxation phenomena in the glass transition. The cc-relaxation temperatures range found in the present study is spread from 105 to 135°C while published glass transition temperatures are in the range 64 to 74°C by DSC and 52 to 65°C by penetrometry. Those differences in temperature ranges show that if cc-relaxation and glass transition are two related phenomena, they are not to be confused. Usually, T, and Tgcan be separated taking into account that the former is mainly a function of w and the latter a function of both texpand dT/dt. 5.2.4 Reversibility of the alpha relaxation. In order to illustrate experimentally the cc-relaxation reversibility, two isochronal temperature-scans were done by successive decrease and

petroleum

pitch

1017

increase of temperature. Although temperature-scan experiments are not advised due to extension effect of the geometry, qualitative analysis can be gained from such results. The obtained isochrones are presented in Figs 3 and 5. It is clearly shown that the c(relaxation phenomenon is reversible and the second step obtained during quenching is observed with the same amplitude. Nevertheless, if temperature-scan and frequency-scan curves are superimposed on each other at low temperatures, the former ones are above the latter ones as the cc-relaxation proceeds illustrating the effect of texpchange. Correspondingly, the tan (6) temperature-scan peaks show a reduced amplitude as a consequence of ageing from decreasing to increasing temperature (the frequency-scan points can be seen as no-aged results). A slight and reversible phenomenon can also be observed in those temperature-scan curves: a small plateau is present at the inflexion point G’ in the range from 117 to 119°C. Correspondingly, a second reversible and small peak is observed in Fig. 5 at this inflexion point temperature. This slight phenomenon could be attributed to p-relaxation but further work is needed for clear identification of such phenomenon. 5.3 Time-temperature superposition The standard procedure described by Ferry [ 1 l] concerning polymers was applied to the A240 obtained results. First, a reference temperature T, of 120°C was chosen to which all the other data are to be shifted in order to achieve contiguity at the reduced temperature. The horizontal distance corresponding to each shift is commonly named as the shift factor and noted as aT. The reference temperature can be chosen among all working temperatures: the obtained results can be easily transposable to any other reference temperature as explained by Rand [2]. Each viscoelastic modulus is corrected as follows: G, = GTIT, PJP

(8)

Therefore, this correction can be achieved if the temperature-dependence of the material density is known. To our knowledge, no data have been published in this field for Ashland A240. Nevertheless, this density is expected to vary within the range from 1200 to 1500 kg. m-3 which is a sufficiently slight variation to be neglected for a first approximation. As done by previous authors [ 11, all the shift factors aT were determined from the loss moduli data without correction for change in specific gravity. Then, this reduced modulus is plotted logarithmically against the reduced frequency w. aT product of the shift factor and the regular frequency. Therefore, the obtained single curves are plotted using a reduced frequency horizontal axis resulting from the different shifts. As the loss modulus data are usually more accurate, particularly at low frequency, i.e. at high temperature [ 1,111, the shift factor obtained from the G” data are usually used for superposing all the other viscoelastic parameters as shown in Fig. 6.

X. Pi et al.

1018

-3

~1

1

7

5

3

9

log(a.10) Fig. 6. Master curves for Ashland A240 reduced to 120 C (experiments done under controlled stress). Nevertheless,

this procedure

could

mask

some

infor-

of the WLF method. Therefore, we have chosen to present and compare together the shift factors obtained from the different viscoelastic functions independently. The obtained shift factor values are strictly equivalent for the loss modulus and the dynamic viscosity but, as shown in Fig. 7, those obtained for the storage modulus present an asymptotic value for all temperature above r,. This effect is due to the fact that the storage modulus evolution decreases as the temperature increases above T,: as the pitch has proceeded through the a-relaxation, its storage behaviour becomes temperature-independent. Moreover, one can observe from Fig. 7 the change of slope of the linear temperature dependence of the loss modulus mation

on

the

applicability

shift factor at the same temperature. This breakdown of the time-temperature superposition principle is commonly observed for miscible polymers in the glass transition region [ 131. It is very satisfactory to observe in Fig. 7 how well stress and strain shift factors superpose on each other. Moreover, the c(relaxation effect on G’ is observed for both experimental procedures. Considering the criterion (2) for the applicability of the WLF procedure, those results lead to the fact that it is only applicable at temperatures lower than T, for isotropic pitch A240. Nevertheless, the (3) condition is well fulfilled: the storage shift factor is in total agreement with the experimental observations. The deviation from the WLF procedure seems to be not only the fact for isotropic pitches: Sakai et ui. [9] have also shown deviations for mesophase pitches obtained from A240. Finally, comparison in Fig. 8 with the results previously published by Turpin et al. [ 1] and Sakai et ul. [4] concerning the loss modulus leads to the conclusion that both geometries (plate/plate and cone/plate) are fairly equivalent. 5.4 Non-Debye behclviour criterion In the literature concerning amorphous polymers, the shape of the loss modulus isotherms near the a peak is commonly characterized by two shape parameters: m and n (O
tu
d log(G”)/dcrJ - -n

w>>T,'

(9)

A simple Debye relaxation is given for m = n = 1 while usual values observed for polymers and low-molecular-weight liquids are m - I and 0
4

4

3

3

2 2 1

-2 -2

-3

-4

-3 80

100

120

140

lbrl

180

Fig. 7. Shaft factors as a function of temperature: son betncen experiments done under controlled controlled strain.

80

100

120

140

160

180

T ("0

T("C)

comparrstress and

Fig. 8. Loss modulus shift factor as a function of temperature, comparison with literature; solid symbols, this work; open symbols, Turpin er (11.[ 11; (&) Sakai et d. [4].

Alpha-relaxation of an isotropic petroleum pitch Tammann-Vogel-Fulcher

2

-2

-4 2 -6

-8

-10

-12 9

11

13

15

17

lOOO/(T-To)

Fig. 9.

equation

(eqn (10)).

r, = rmOexp (AU; ‘/(T-

0

5

1019

Isotropic

A240 a-relaxation Fulcher plot.

Tammann-Vogel-

mentioned above, one of the most important features of the a-relaxation is its non-Debye behaviour (m,n) #( 1,l) in the frequency dependence of the characteristic parameters. A low frequency tail (parameter m) has been estimated from the five highest temperature isotherms (from 120 to 160°C) and a high frequency tail (parameter n) has been calculated from the G” isotherm obtained at 94.6”C (Fig. 2). The obtained values are m = 1 and n = 0.43 which fall within the low-molecular-weight liquids range mentioned above. Therefore, the observed relaxation of the isotropic A240 fulfils the (4) criterion for doidentification. 5.5 z, non-Arrhenius temperature-dependence criterion As mentioned above, the best parameter to characterise the glass transition should be r,,,. Moreover, ra and r,O1 values are of the same order of magnitude and the former can be estimated from the oscillatory rheometry results. As a matter of fact, the low temperature frequency-scan isotherms of the loss modulus present a maximum which corresponds to w. t, = 1 [ 151. For the curves without maximum, especially at high temperatures, the above estimated shift factors are used to estimate 7,. The temperaturedependence of r, is presented in Fig. 9, illustrating its non-Arrhenius behaviour. This phenomenon is usual for amorphous polymers and can be well parametrized by means of the following Table 1. Parameters

Material/param. PH PVAc Usual range Isotropic A240

(10)

The temperature r,, has been fitted in order to optimise the correlation coefficient: the respective obtained values are To= 30°C Acc,=6.7 x lO-4 K-l, t,,,= 1.3 x lo-” s and the correlation coefficient is r=0.992. A similar analysis using the Arrhenius equation has been tested and was clearly non-linear. Therefore, the criterion (5) mentioned above is well satisfied. Obtained values of To, T,, Act, and rao are compared with those usually obtained for amorphous polymers [ 151 and to those published for poly(2-hydroxypropyl ether bisphenol A) referenced as PH and poly(viny1 acetate) referenced as PVAc [ 121 in Table 1. Those results show that, except for to, the A240 isotropic pitch c(relaxation characteristics fall within the usual values of amorphous polymers and especially within those of the PH and PVAc. Concerning the r. parameter, the A240 value is found to be 10’ time higher than that published for PVAc and lo3 time higher than the usual value observed for amorphous polymers. This could be explained by the characteristic molecular scale of those species: the isotropic A240 pitch is composed of small molecular units, smaller than those of PVAc which are themselves smaller than those of PH.

T-Tr -40

-20

0

20

40

60

0

-20

I I

._l

-60

( “@

~

1 o from G”, present l

from G”, Turpin

q

from G’, present

work et al. [l]

~ 0

work

q

-100

Fig. 10. Williams, Landel and Ferry plot reduced to 120°C: open symbols present work; solid symbols, Turpin et al. [I].

characterizing the cc-relaxation of various the A240 isotropic pitch 50 (s) 3.2 x lo-l3 lo-l2 lo-l3 1.3 X lo-‘0

T,,))

Act, (K-l) 10.4 x 1o-4 7 X 10-d 5 x 10-d 6.7 x 1O-4

amorphous

T, (“C) 75 -7 30

polymers

and

Ts- T, (“C) 22 49 50 22-44

x. PY et al.

1020 Table 2. Williams,

Landel

and Ferry parameters

for isotropic

Turpin et (11. [ I] Plate/plate 411.05 Controlled stress 11.4 145.7

Sakai er ul. [4] Plate/plate 1.3/0.6 1.7/0.4 Controlled strain 13.5 136.6

Param./authors Exp. geometry (cm) Diameter/gap Exp. procedure C, C,

5.6 Williams, Landel and Ferry procedure The WLF procedure was applied to the above results (eqn (11)) in order to compare the order of magnitude of the corresponding parameters (C,, C,) to those available in the literature [ 1,9]. log(a,)=

-c,

(T- T,)/(C, + T-T,)

A240 at T, = 120’C and from different

(11)

Temperature dependence of the shift factor criterion is plotted in Fig. 10 for the selected temperature of 120°C and compared to those available in the literature [ 11, The linearity of the loss modulus shift factor criterion is fairly obtained but the behaviour of the storage modulus shift factor criterion is drastically different above T,.Therefore, and as usually done, the WLF parameters were estimated from the loss modulus criterion. They were gathered and compared to the published results in Table 2. Those results show clearly that even if the shift factor results of the different studies are fairly comparable, the WLF linearity parameters are quite different. Nevertheless, C, and C’, values are in the same order of magnitude. Based on data fitting on a large number of polymers, fixed values of C,, = 8.86 and C,, = 101.6 were used in conjunction with a reference temperature T,,which was allowed to be an adjustable parameter but generally fell about 50°C above Tg [9]. This approximation has been widely used and composite data for many different polymers are described with the single adjustable parameter T,. To our knowledge, only one author has tried to use this approximation to A240 isotropic pitch [9] and the obtained fitting temperature value was 155°C. This approximation has been applied to our results with success and the fitting temperature value was 120°C which is very close to T,and T,. 6. CONCLUSIONS

Controlled stress and controlled strain oscillatory measurements can be considered as equivalent experimental procedures for isotropic pitch materials. Moreover, plate/plate and cone/plate experimental devices associated with various gap width lead to similar results. A relaxation is observed at 114°C as a three decades storage modulus isochrone step and at 124°C as a 11 units peak of tan (6) isochrone. As this relaxation fulfils both the non-Debye and nonArrhenius criteria, it is well-identified as an alpharelaxation. The applicability criteria of the WLF method are well fulfilled at temperature lower than 124°C for the A240 isotropic petroleum pitch. At

authors

and geometries

Present work Cone/plate 2.5/0.005 Strain, stress 7 85

Mean values

10.6 122.5

higher temperature, the storage shift factor reaches asymptotic value as the pitch has proceeded through the cc-relaxation phenomena toward the pseudoNewtonian viscous liquid state. The TVF characteristic parameters of the observed a-relaxation characteristic time are very similar to those published for amorphous polymers. Temperature-scan experiments lead to observations of potential ageing and ,0-

7. NOTATIONS

w

shift factor WLF constants storage modulus loss modulus high and low frequency tail parameters characteristic experimental time tan (6) peak maximum temperature alpha relaxation, reference and glass transition temperatures softening point temperature Kauzmann temperature linear coefficient of thermal volume expansion phase-lag dynamic viscosity strain specific gravity, reference specific gravity stress alpha, beta and molecular relaxation times frequency

_ -, Km’ Pa Pa Pa.s S

"C "C

"C "C K-r rad Pa.s

kg,rn-’ Pa S

rad,s-’

REFERENCES 1. Turpin, M., Cheung, T. and Rand, B., C&on, 1994, 32, 225. 2. Rand, B.. Fuel, 1987, 66. 1491. 3. Nazem, F.F., Fuel, 1980, 59, 851. 4. Sakai. M. and Inaeaki. M.. Carbon. 1981, 19. 37 5. Cheung, T., Turpm, M. and Rand; B., C&on, 1996, 34, 265. 6. Daji, J., Rand, B. and Turpin, M., in Extended Abstracts Carbon ‘96, Vol. 1. The British Carbon Group, Newcastle, U.K., 1996, pp. 140&141. 7. Narciso-Romero, F. J., Fleurot, O., Martin, V.,

Alpha-relaxation

8.

9. 10. 11. 12.

of an isotropic

Edie, D., McHugh, J. and RodriguezReinoso, F., in Extended Abstracts Carbon ‘96. Vol. 2. The British Carbon Group, Newcastle, U.K.; 1996, pp. 561-562. Fleurot, 0. and Edie, D. D., in Extended Abstracts Carbon ‘96, Vol. 2. The British Carbon Group, Newcastle, U.K., 1996. pp. 425-426. Sakai, M., Sat&- Y. and Inagaki, M., in Extended Abstracts Carbon ‘90. Paris. France. 1990. ._ DD. 298-299. Hara, R., in Extended Abstracts Carbon ‘90, Paris, France, 1990, pp. 290-291. Ferry, J.D., Viscoelastic properties of Polymers, Wiley, New York, 1961. Alegria, A., Guerrica-Echevarria, E., Goitiandia, L.,

13. 14. 15. 16. 17. 18.

petroleum

pitch

1021

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